Properties

Label 8008.2.a.y.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.53687\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.53687 q^{3} -0.216819 q^{5} +1.00000 q^{7} -0.638026 q^{9} +O(q^{10})\) \(q-1.53687 q^{3} -0.216819 q^{5} +1.00000 q^{7} -0.638026 q^{9} -1.00000 q^{11} -1.00000 q^{13} +0.333223 q^{15} +1.18307 q^{17} +7.88361 q^{19} -1.53687 q^{21} -1.22149 q^{23} -4.95299 q^{25} +5.59118 q^{27} -5.20441 q^{29} -4.80232 q^{31} +1.53687 q^{33} -0.216819 q^{35} +8.61831 q^{37} +1.53687 q^{39} -7.95896 q^{41} -3.91246 q^{43} +0.138336 q^{45} +3.51062 q^{47} +1.00000 q^{49} -1.81822 q^{51} +6.35917 q^{53} +0.216819 q^{55} -12.1161 q^{57} -4.23350 q^{59} -0.624073 q^{61} -0.638026 q^{63} +0.216819 q^{65} +4.74600 q^{67} +1.87727 q^{69} -13.7254 q^{71} +16.1174 q^{73} +7.61211 q^{75} -1.00000 q^{77} +13.0838 q^{79} -6.67884 q^{81} -3.48532 q^{83} -0.256512 q^{85} +7.99850 q^{87} +3.11011 q^{89} -1.00000 q^{91} +7.38054 q^{93} -1.70932 q^{95} -3.26128 q^{97} +0.638026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.53687 −0.887313 −0.443657 0.896197i \(-0.646319\pi\)
−0.443657 + 0.896197i \(0.646319\pi\)
\(4\) 0 0
\(5\) −0.216819 −0.0969644 −0.0484822 0.998824i \(-0.515438\pi\)
−0.0484822 + 0.998824i \(0.515438\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −0.638026 −0.212675
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.333223 0.0860378
\(16\) 0 0
\(17\) 1.18307 0.286936 0.143468 0.989655i \(-0.454175\pi\)
0.143468 + 0.989655i \(0.454175\pi\)
\(18\) 0 0
\(19\) 7.88361 1.80862 0.904312 0.426872i \(-0.140385\pi\)
0.904312 + 0.426872i \(0.140385\pi\)
\(20\) 0 0
\(21\) −1.53687 −0.335373
\(22\) 0 0
\(23\) −1.22149 −0.254698 −0.127349 0.991858i \(-0.540647\pi\)
−0.127349 + 0.991858i \(0.540647\pi\)
\(24\) 0 0
\(25\) −4.95299 −0.990598
\(26\) 0 0
\(27\) 5.59118 1.07602
\(28\) 0 0
\(29\) −5.20441 −0.966434 −0.483217 0.875501i \(-0.660532\pi\)
−0.483217 + 0.875501i \(0.660532\pi\)
\(30\) 0 0
\(31\) −4.80232 −0.862522 −0.431261 0.902227i \(-0.641931\pi\)
−0.431261 + 0.902227i \(0.641931\pi\)
\(32\) 0 0
\(33\) 1.53687 0.267535
\(34\) 0 0
\(35\) −0.216819 −0.0366491
\(36\) 0 0
\(37\) 8.61831 1.41684 0.708420 0.705791i \(-0.249408\pi\)
0.708420 + 0.705791i \(0.249408\pi\)
\(38\) 0 0
\(39\) 1.53687 0.246096
\(40\) 0 0
\(41\) −7.95896 −1.24298 −0.621490 0.783422i \(-0.713472\pi\)
−0.621490 + 0.783422i \(0.713472\pi\)
\(42\) 0 0
\(43\) −3.91246 −0.596644 −0.298322 0.954465i \(-0.596427\pi\)
−0.298322 + 0.954465i \(0.596427\pi\)
\(44\) 0 0
\(45\) 0.138336 0.0206219
\(46\) 0 0
\(47\) 3.51062 0.512077 0.256038 0.966667i \(-0.417583\pi\)
0.256038 + 0.966667i \(0.417583\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.81822 −0.254602
\(52\) 0 0
\(53\) 6.35917 0.873499 0.436750 0.899583i \(-0.356130\pi\)
0.436750 + 0.899583i \(0.356130\pi\)
\(54\) 0 0
\(55\) 0.216819 0.0292359
\(56\) 0 0
\(57\) −12.1161 −1.60482
\(58\) 0 0
\(59\) −4.23350 −0.551155 −0.275577 0.961279i \(-0.588869\pi\)
−0.275577 + 0.961279i \(0.588869\pi\)
\(60\) 0 0
\(61\) −0.624073 −0.0799043 −0.0399522 0.999202i \(-0.512721\pi\)
−0.0399522 + 0.999202i \(0.512721\pi\)
\(62\) 0 0
\(63\) −0.638026 −0.0803837
\(64\) 0 0
\(65\) 0.216819 0.0268931
\(66\) 0 0
\(67\) 4.74600 0.579817 0.289908 0.957054i \(-0.406375\pi\)
0.289908 + 0.957054i \(0.406375\pi\)
\(68\) 0 0
\(69\) 1.87727 0.225997
\(70\) 0 0
\(71\) −13.7254 −1.62890 −0.814452 0.580231i \(-0.802962\pi\)
−0.814452 + 0.580231i \(0.802962\pi\)
\(72\) 0 0
\(73\) 16.1174 1.88640 0.943202 0.332220i \(-0.107798\pi\)
0.943202 + 0.332220i \(0.107798\pi\)
\(74\) 0 0
\(75\) 7.61211 0.878971
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 13.0838 1.47204 0.736019 0.676960i \(-0.236703\pi\)
0.736019 + 0.676960i \(0.236703\pi\)
\(80\) 0 0
\(81\) −6.67884 −0.742094
\(82\) 0 0
\(83\) −3.48532 −0.382564 −0.191282 0.981535i \(-0.561265\pi\)
−0.191282 + 0.981535i \(0.561265\pi\)
\(84\) 0 0
\(85\) −0.256512 −0.0278226
\(86\) 0 0
\(87\) 7.99850 0.857530
\(88\) 0 0
\(89\) 3.11011 0.329671 0.164836 0.986321i \(-0.447291\pi\)
0.164836 + 0.986321i \(0.447291\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 7.38054 0.765327
\(94\) 0 0
\(95\) −1.70932 −0.175372
\(96\) 0 0
\(97\) −3.26128 −0.331133 −0.165567 0.986199i \(-0.552945\pi\)
−0.165567 + 0.986199i \(0.552945\pi\)
\(98\) 0 0
\(99\) 0.638026 0.0641240
\(100\) 0 0
\(101\) 11.7866 1.17281 0.586406 0.810018i \(-0.300542\pi\)
0.586406 + 0.810018i \(0.300542\pi\)
\(102\) 0 0
\(103\) −15.9517 −1.57177 −0.785884 0.618373i \(-0.787792\pi\)
−0.785884 + 0.618373i \(0.787792\pi\)
\(104\) 0 0
\(105\) 0.333223 0.0325192
\(106\) 0 0
\(107\) −4.08272 −0.394691 −0.197346 0.980334i \(-0.563232\pi\)
−0.197346 + 0.980334i \(0.563232\pi\)
\(108\) 0 0
\(109\) −8.93859 −0.856162 −0.428081 0.903740i \(-0.640810\pi\)
−0.428081 + 0.903740i \(0.640810\pi\)
\(110\) 0 0
\(111\) −13.2452 −1.25718
\(112\) 0 0
\(113\) 7.43235 0.699177 0.349588 0.936903i \(-0.386321\pi\)
0.349588 + 0.936903i \(0.386321\pi\)
\(114\) 0 0
\(115\) 0.264842 0.0246967
\(116\) 0 0
\(117\) 0.638026 0.0589855
\(118\) 0 0
\(119\) 1.18307 0.108452
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 12.2319 1.10291
\(124\) 0 0
\(125\) 2.15800 0.193017
\(126\) 0 0
\(127\) 1.10500 0.0980525 0.0490263 0.998797i \(-0.484388\pi\)
0.0490263 + 0.998797i \(0.484388\pi\)
\(128\) 0 0
\(129\) 6.01294 0.529410
\(130\) 0 0
\(131\) −13.4517 −1.17528 −0.587642 0.809121i \(-0.699943\pi\)
−0.587642 + 0.809121i \(0.699943\pi\)
\(132\) 0 0
\(133\) 7.88361 0.683596
\(134\) 0 0
\(135\) −1.21227 −0.104336
\(136\) 0 0
\(137\) 5.13711 0.438893 0.219447 0.975625i \(-0.429575\pi\)
0.219447 + 0.975625i \(0.429575\pi\)
\(138\) 0 0
\(139\) 3.18510 0.270156 0.135078 0.990835i \(-0.456871\pi\)
0.135078 + 0.990835i \(0.456871\pi\)
\(140\) 0 0
\(141\) −5.39537 −0.454372
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.12841 0.0937097
\(146\) 0 0
\(147\) −1.53687 −0.126759
\(148\) 0 0
\(149\) −9.25902 −0.758529 −0.379264 0.925288i \(-0.623823\pi\)
−0.379264 + 0.925288i \(0.623823\pi\)
\(150\) 0 0
\(151\) −6.48990 −0.528141 −0.264070 0.964503i \(-0.585065\pi\)
−0.264070 + 0.964503i \(0.585065\pi\)
\(152\) 0 0
\(153\) −0.754828 −0.0610242
\(154\) 0 0
\(155\) 1.04123 0.0836339
\(156\) 0 0
\(157\) 10.3997 0.829989 0.414995 0.909824i \(-0.363783\pi\)
0.414995 + 0.909824i \(0.363783\pi\)
\(158\) 0 0
\(159\) −9.77323 −0.775068
\(160\) 0 0
\(161\) −1.22149 −0.0962670
\(162\) 0 0
\(163\) −15.6197 −1.22343 −0.611716 0.791077i \(-0.709521\pi\)
−0.611716 + 0.791077i \(0.709521\pi\)
\(164\) 0 0
\(165\) −0.333223 −0.0259414
\(166\) 0 0
\(167\) 17.3584 1.34323 0.671617 0.740898i \(-0.265600\pi\)
0.671617 + 0.740898i \(0.265600\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.02995 −0.384650
\(172\) 0 0
\(173\) −23.0133 −1.74967 −0.874834 0.484422i \(-0.839030\pi\)
−0.874834 + 0.484422i \(0.839030\pi\)
\(174\) 0 0
\(175\) −4.95299 −0.374411
\(176\) 0 0
\(177\) 6.50635 0.489047
\(178\) 0 0
\(179\) −15.2298 −1.13833 −0.569163 0.822225i \(-0.692733\pi\)
−0.569163 + 0.822225i \(0.692733\pi\)
\(180\) 0 0
\(181\) −7.68362 −0.571119 −0.285559 0.958361i \(-0.592179\pi\)
−0.285559 + 0.958361i \(0.592179\pi\)
\(182\) 0 0
\(183\) 0.959120 0.0709002
\(184\) 0 0
\(185\) −1.86861 −0.137383
\(186\) 0 0
\(187\) −1.18307 −0.0865145
\(188\) 0 0
\(189\) 5.59118 0.406698
\(190\) 0 0
\(191\) −22.5121 −1.62892 −0.814459 0.580221i \(-0.802966\pi\)
−0.814459 + 0.580221i \(0.802966\pi\)
\(192\) 0 0
\(193\) 19.9282 1.43446 0.717230 0.696837i \(-0.245410\pi\)
0.717230 + 0.696837i \(0.245410\pi\)
\(194\) 0 0
\(195\) −0.333223 −0.0238626
\(196\) 0 0
\(197\) 20.3502 1.44989 0.724947 0.688804i \(-0.241864\pi\)
0.724947 + 0.688804i \(0.241864\pi\)
\(198\) 0 0
\(199\) 9.68637 0.686648 0.343324 0.939217i \(-0.388447\pi\)
0.343324 + 0.939217i \(0.388447\pi\)
\(200\) 0 0
\(201\) −7.29400 −0.514479
\(202\) 0 0
\(203\) −5.20441 −0.365278
\(204\) 0 0
\(205\) 1.72565 0.120525
\(206\) 0 0
\(207\) 0.779343 0.0541681
\(208\) 0 0
\(209\) −7.88361 −0.545321
\(210\) 0 0
\(211\) −8.97542 −0.617893 −0.308947 0.951079i \(-0.599976\pi\)
−0.308947 + 0.951079i \(0.599976\pi\)
\(212\) 0 0
\(213\) 21.0942 1.44535
\(214\) 0 0
\(215\) 0.848295 0.0578532
\(216\) 0 0
\(217\) −4.80232 −0.326003
\(218\) 0 0
\(219\) −24.7704 −1.67383
\(220\) 0 0
\(221\) −1.18307 −0.0795817
\(222\) 0 0
\(223\) 14.5413 0.973760 0.486880 0.873469i \(-0.338135\pi\)
0.486880 + 0.873469i \(0.338135\pi\)
\(224\) 0 0
\(225\) 3.16014 0.210676
\(226\) 0 0
\(227\) −7.69756 −0.510905 −0.255453 0.966822i \(-0.582224\pi\)
−0.255453 + 0.966822i \(0.582224\pi\)
\(228\) 0 0
\(229\) 21.9995 1.45377 0.726883 0.686761i \(-0.240968\pi\)
0.726883 + 0.686761i \(0.240968\pi\)
\(230\) 0 0
\(231\) 1.53687 0.101119
\(232\) 0 0
\(233\) 19.1946 1.25748 0.628739 0.777617i \(-0.283571\pi\)
0.628739 + 0.777617i \(0.283571\pi\)
\(234\) 0 0
\(235\) −0.761169 −0.0496532
\(236\) 0 0
\(237\) −20.1081 −1.30616
\(238\) 0 0
\(239\) 6.74464 0.436274 0.218137 0.975918i \(-0.430002\pi\)
0.218137 + 0.975918i \(0.430002\pi\)
\(240\) 0 0
\(241\) −16.1910 −1.04296 −0.521478 0.853264i \(-0.674619\pi\)
−0.521478 + 0.853264i \(0.674619\pi\)
\(242\) 0 0
\(243\) −6.50901 −0.417553
\(244\) 0 0
\(245\) −0.216819 −0.0138521
\(246\) 0 0
\(247\) −7.88361 −0.501622
\(248\) 0 0
\(249\) 5.35650 0.339454
\(250\) 0 0
\(251\) −8.71405 −0.550026 −0.275013 0.961440i \(-0.588682\pi\)
−0.275013 + 0.961440i \(0.588682\pi\)
\(252\) 0 0
\(253\) 1.22149 0.0767945
\(254\) 0 0
\(255\) 0.394225 0.0246873
\(256\) 0 0
\(257\) −21.6186 −1.34853 −0.674265 0.738489i \(-0.735540\pi\)
−0.674265 + 0.738489i \(0.735540\pi\)
\(258\) 0 0
\(259\) 8.61831 0.535515
\(260\) 0 0
\(261\) 3.32055 0.205537
\(262\) 0 0
\(263\) −16.8633 −1.03984 −0.519918 0.854216i \(-0.674038\pi\)
−0.519918 + 0.854216i \(0.674038\pi\)
\(264\) 0 0
\(265\) −1.37879 −0.0846984
\(266\) 0 0
\(267\) −4.77984 −0.292522
\(268\) 0 0
\(269\) 7.95831 0.485227 0.242613 0.970123i \(-0.421995\pi\)
0.242613 + 0.970123i \(0.421995\pi\)
\(270\) 0 0
\(271\) 2.64947 0.160944 0.0804719 0.996757i \(-0.474357\pi\)
0.0804719 + 0.996757i \(0.474357\pi\)
\(272\) 0 0
\(273\) 1.53687 0.0930157
\(274\) 0 0
\(275\) 4.95299 0.298677
\(276\) 0 0
\(277\) −15.8295 −0.951103 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(278\) 0 0
\(279\) 3.06400 0.183437
\(280\) 0 0
\(281\) 13.7268 0.818871 0.409436 0.912339i \(-0.365726\pi\)
0.409436 + 0.912339i \(0.365726\pi\)
\(282\) 0 0
\(283\) −33.1130 −1.96836 −0.984181 0.177169i \(-0.943306\pi\)
−0.984181 + 0.177169i \(0.943306\pi\)
\(284\) 0 0
\(285\) 2.62700 0.155610
\(286\) 0 0
\(287\) −7.95896 −0.469802
\(288\) 0 0
\(289\) −15.6004 −0.917668
\(290\) 0 0
\(291\) 5.01217 0.293819
\(292\) 0 0
\(293\) −30.8767 −1.80384 −0.901919 0.431905i \(-0.857842\pi\)
−0.901919 + 0.431905i \(0.857842\pi\)
\(294\) 0 0
\(295\) 0.917903 0.0534424
\(296\) 0 0
\(297\) −5.59118 −0.324433
\(298\) 0 0
\(299\) 1.22149 0.0706406
\(300\) 0 0
\(301\) −3.91246 −0.225510
\(302\) 0 0
\(303\) −18.1145 −1.04065
\(304\) 0 0
\(305\) 0.135311 0.00774788
\(306\) 0 0
\(307\) −30.9074 −1.76398 −0.881990 0.471268i \(-0.843796\pi\)
−0.881990 + 0.471268i \(0.843796\pi\)
\(308\) 0 0
\(309\) 24.5157 1.39465
\(310\) 0 0
\(311\) 21.5426 1.22157 0.610785 0.791796i \(-0.290854\pi\)
0.610785 + 0.791796i \(0.290854\pi\)
\(312\) 0 0
\(313\) −26.1297 −1.47694 −0.738470 0.674286i \(-0.764451\pi\)
−0.738470 + 0.674286i \(0.764451\pi\)
\(314\) 0 0
\(315\) 0.138336 0.00779436
\(316\) 0 0
\(317\) −17.7543 −0.997179 −0.498590 0.866838i \(-0.666148\pi\)
−0.498590 + 0.866838i \(0.666148\pi\)
\(318\) 0 0
\(319\) 5.20441 0.291391
\(320\) 0 0
\(321\) 6.27461 0.350215
\(322\) 0 0
\(323\) 9.32684 0.518959
\(324\) 0 0
\(325\) 4.95299 0.274742
\(326\) 0 0
\(327\) 13.7375 0.759684
\(328\) 0 0
\(329\) 3.51062 0.193547
\(330\) 0 0
\(331\) 6.34621 0.348819 0.174410 0.984673i \(-0.444198\pi\)
0.174410 + 0.984673i \(0.444198\pi\)
\(332\) 0 0
\(333\) −5.49870 −0.301327
\(334\) 0 0
\(335\) −1.02902 −0.0562216
\(336\) 0 0
\(337\) −24.4535 −1.33206 −0.666032 0.745923i \(-0.732009\pi\)
−0.666032 + 0.745923i \(0.732009\pi\)
\(338\) 0 0
\(339\) −11.4226 −0.620389
\(340\) 0 0
\(341\) 4.80232 0.260060
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −0.407029 −0.0219137
\(346\) 0 0
\(347\) −15.7975 −0.848057 −0.424028 0.905649i \(-0.639384\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(348\) 0 0
\(349\) −11.3768 −0.608988 −0.304494 0.952514i \(-0.598487\pi\)
−0.304494 + 0.952514i \(0.598487\pi\)
\(350\) 0 0
\(351\) −5.59118 −0.298435
\(352\) 0 0
\(353\) 25.1377 1.33795 0.668973 0.743287i \(-0.266734\pi\)
0.668973 + 0.743287i \(0.266734\pi\)
\(354\) 0 0
\(355\) 2.97593 0.157946
\(356\) 0 0
\(357\) −1.81822 −0.0962306
\(358\) 0 0
\(359\) 19.7034 1.03991 0.519954 0.854195i \(-0.325949\pi\)
0.519954 + 0.854195i \(0.325949\pi\)
\(360\) 0 0
\(361\) 43.1513 2.27112
\(362\) 0 0
\(363\) −1.53687 −0.0806648
\(364\) 0 0
\(365\) −3.49457 −0.182914
\(366\) 0 0
\(367\) 3.32182 0.173398 0.0866988 0.996235i \(-0.472368\pi\)
0.0866988 + 0.996235i \(0.472368\pi\)
\(368\) 0 0
\(369\) 5.07802 0.264351
\(370\) 0 0
\(371\) 6.35917 0.330152
\(372\) 0 0
\(373\) 3.60634 0.186729 0.0933645 0.995632i \(-0.470238\pi\)
0.0933645 + 0.995632i \(0.470238\pi\)
\(374\) 0 0
\(375\) −3.31656 −0.171267
\(376\) 0 0
\(377\) 5.20441 0.268041
\(378\) 0 0
\(379\) 6.21587 0.319288 0.159644 0.987175i \(-0.448965\pi\)
0.159644 + 0.987175i \(0.448965\pi\)
\(380\) 0 0
\(381\) −1.69824 −0.0870033
\(382\) 0 0
\(383\) −11.4018 −0.582607 −0.291303 0.956631i \(-0.594089\pi\)
−0.291303 + 0.956631i \(0.594089\pi\)
\(384\) 0 0
\(385\) 0.216819 0.0110501
\(386\) 0 0
\(387\) 2.49625 0.126891
\(388\) 0 0
\(389\) −13.4648 −0.682692 −0.341346 0.939938i \(-0.610883\pi\)
−0.341346 + 0.939938i \(0.610883\pi\)
\(390\) 0 0
\(391\) −1.44511 −0.0730822
\(392\) 0 0
\(393\) 20.6736 1.04284
\(394\) 0 0
\(395\) −2.83681 −0.142735
\(396\) 0 0
\(397\) 15.9250 0.799254 0.399627 0.916678i \(-0.369140\pi\)
0.399627 + 0.916678i \(0.369140\pi\)
\(398\) 0 0
\(399\) −12.1161 −0.606563
\(400\) 0 0
\(401\) 7.83195 0.391109 0.195555 0.980693i \(-0.437349\pi\)
0.195555 + 0.980693i \(0.437349\pi\)
\(402\) 0 0
\(403\) 4.80232 0.239220
\(404\) 0 0
\(405\) 1.44810 0.0719567
\(406\) 0 0
\(407\) −8.61831 −0.427194
\(408\) 0 0
\(409\) −31.3616 −1.55073 −0.775367 0.631511i \(-0.782435\pi\)
−0.775367 + 0.631511i \(0.782435\pi\)
\(410\) 0 0
\(411\) −7.89508 −0.389436
\(412\) 0 0
\(413\) −4.23350 −0.208317
\(414\) 0 0
\(415\) 0.755685 0.0370951
\(416\) 0 0
\(417\) −4.89508 −0.239713
\(418\) 0 0
\(419\) 32.0041 1.56350 0.781751 0.623591i \(-0.214327\pi\)
0.781751 + 0.623591i \(0.214327\pi\)
\(420\) 0 0
\(421\) −11.0636 −0.539208 −0.269604 0.962971i \(-0.586893\pi\)
−0.269604 + 0.962971i \(0.586893\pi\)
\(422\) 0 0
\(423\) −2.23987 −0.108906
\(424\) 0 0
\(425\) −5.85972 −0.284238
\(426\) 0 0
\(427\) −0.624073 −0.0302010
\(428\) 0 0
\(429\) −1.53687 −0.0742009
\(430\) 0 0
\(431\) −17.5456 −0.845142 −0.422571 0.906330i \(-0.638872\pi\)
−0.422571 + 0.906330i \(0.638872\pi\)
\(432\) 0 0
\(433\) 36.7819 1.76763 0.883814 0.467839i \(-0.154967\pi\)
0.883814 + 0.467839i \(0.154967\pi\)
\(434\) 0 0
\(435\) −1.73423 −0.0831499
\(436\) 0 0
\(437\) −9.62975 −0.460654
\(438\) 0 0
\(439\) −4.35920 −0.208053 −0.104027 0.994575i \(-0.533173\pi\)
−0.104027 + 0.994575i \(0.533173\pi\)
\(440\) 0 0
\(441\) −0.638026 −0.0303822
\(442\) 0 0
\(443\) −9.75163 −0.463314 −0.231657 0.972798i \(-0.574415\pi\)
−0.231657 + 0.972798i \(0.574415\pi\)
\(444\) 0 0
\(445\) −0.674331 −0.0319664
\(446\) 0 0
\(447\) 14.2299 0.673052
\(448\) 0 0
\(449\) −7.07433 −0.333858 −0.166929 0.985969i \(-0.553385\pi\)
−0.166929 + 0.985969i \(0.553385\pi\)
\(450\) 0 0
\(451\) 7.95896 0.374773
\(452\) 0 0
\(453\) 9.97415 0.468626
\(454\) 0 0
\(455\) 0.216819 0.0101646
\(456\) 0 0
\(457\) 18.9154 0.884823 0.442412 0.896812i \(-0.354123\pi\)
0.442412 + 0.896812i \(0.354123\pi\)
\(458\) 0 0
\(459\) 6.61474 0.308750
\(460\) 0 0
\(461\) −8.96871 −0.417714 −0.208857 0.977946i \(-0.566974\pi\)
−0.208857 + 0.977946i \(0.566974\pi\)
\(462\) 0 0
\(463\) −10.7098 −0.497728 −0.248864 0.968538i \(-0.580057\pi\)
−0.248864 + 0.968538i \(0.580057\pi\)
\(464\) 0 0
\(465\) −1.60024 −0.0742094
\(466\) 0 0
\(467\) −28.1611 −1.30314 −0.651571 0.758588i \(-0.725890\pi\)
−0.651571 + 0.758588i \(0.725890\pi\)
\(468\) 0 0
\(469\) 4.74600 0.219150
\(470\) 0 0
\(471\) −15.9831 −0.736460
\(472\) 0 0
\(473\) 3.91246 0.179895
\(474\) 0 0
\(475\) −39.0474 −1.79162
\(476\) 0 0
\(477\) −4.05732 −0.185772
\(478\) 0 0
\(479\) 2.12403 0.0970494 0.0485247 0.998822i \(-0.484548\pi\)
0.0485247 + 0.998822i \(0.484548\pi\)
\(480\) 0 0
\(481\) −8.61831 −0.392961
\(482\) 0 0
\(483\) 1.87727 0.0854189
\(484\) 0 0
\(485\) 0.707108 0.0321081
\(486\) 0 0
\(487\) 20.5415 0.930822 0.465411 0.885095i \(-0.345907\pi\)
0.465411 + 0.885095i \(0.345907\pi\)
\(488\) 0 0
\(489\) 24.0055 1.08557
\(490\) 0 0
\(491\) −6.18566 −0.279155 −0.139577 0.990211i \(-0.544574\pi\)
−0.139577 + 0.990211i \(0.544574\pi\)
\(492\) 0 0
\(493\) −6.15717 −0.277305
\(494\) 0 0
\(495\) −0.138336 −0.00621775
\(496\) 0 0
\(497\) −13.7254 −0.615668
\(498\) 0 0
\(499\) −5.87923 −0.263190 −0.131595 0.991304i \(-0.542010\pi\)
−0.131595 + 0.991304i \(0.542010\pi\)
\(500\) 0 0
\(501\) −26.6777 −1.19187
\(502\) 0 0
\(503\) −40.7941 −1.81892 −0.909460 0.415791i \(-0.863505\pi\)
−0.909460 + 0.415791i \(0.863505\pi\)
\(504\) 0 0
\(505\) −2.55556 −0.113721
\(506\) 0 0
\(507\) −1.53687 −0.0682549
\(508\) 0 0
\(509\) −25.7132 −1.13972 −0.569858 0.821743i \(-0.693002\pi\)
−0.569858 + 0.821743i \(0.693002\pi\)
\(510\) 0 0
\(511\) 16.1174 0.712994
\(512\) 0 0
\(513\) 44.0787 1.94612
\(514\) 0 0
\(515\) 3.45863 0.152406
\(516\) 0 0
\(517\) −3.51062 −0.154397
\(518\) 0 0
\(519\) 35.3685 1.55250
\(520\) 0 0
\(521\) −35.0574 −1.53589 −0.767947 0.640513i \(-0.778722\pi\)
−0.767947 + 0.640513i \(0.778722\pi\)
\(522\) 0 0
\(523\) −27.2540 −1.19174 −0.595868 0.803082i \(-0.703192\pi\)
−0.595868 + 0.803082i \(0.703192\pi\)
\(524\) 0 0
\(525\) 7.61211 0.332220
\(526\) 0 0
\(527\) −5.68147 −0.247489
\(528\) 0 0
\(529\) −21.5080 −0.935129
\(530\) 0 0
\(531\) 2.70108 0.117217
\(532\) 0 0
\(533\) 7.95896 0.344741
\(534\) 0 0
\(535\) 0.885210 0.0382710
\(536\) 0 0
\(537\) 23.4062 1.01005
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −40.6761 −1.74880 −0.874401 0.485204i \(-0.838745\pi\)
−0.874401 + 0.485204i \(0.838745\pi\)
\(542\) 0 0
\(543\) 11.8087 0.506761
\(544\) 0 0
\(545\) 1.93806 0.0830172
\(546\) 0 0
\(547\) 35.1108 1.50123 0.750615 0.660740i \(-0.229758\pi\)
0.750615 + 0.660740i \(0.229758\pi\)
\(548\) 0 0
\(549\) 0.398175 0.0169937
\(550\) 0 0
\(551\) −41.0295 −1.74792
\(552\) 0 0
\(553\) 13.0838 0.556378
\(554\) 0 0
\(555\) 2.87182 0.121902
\(556\) 0 0
\(557\) −38.7242 −1.64080 −0.820399 0.571791i \(-0.806249\pi\)
−0.820399 + 0.571791i \(0.806249\pi\)
\(558\) 0 0
\(559\) 3.91246 0.165479
\(560\) 0 0
\(561\) 1.81822 0.0767654
\(562\) 0 0
\(563\) −27.6682 −1.16608 −0.583038 0.812445i \(-0.698136\pi\)
−0.583038 + 0.812445i \(0.698136\pi\)
\(564\) 0 0
\(565\) −1.61147 −0.0677952
\(566\) 0 0
\(567\) −6.67884 −0.280485
\(568\) 0 0
\(569\) 24.3371 1.02026 0.510132 0.860096i \(-0.329597\pi\)
0.510132 + 0.860096i \(0.329597\pi\)
\(570\) 0 0
\(571\) −4.19074 −0.175377 −0.0876886 0.996148i \(-0.527948\pi\)
−0.0876886 + 0.996148i \(0.527948\pi\)
\(572\) 0 0
\(573\) 34.5982 1.44536
\(574\) 0 0
\(575\) 6.05003 0.252304
\(576\) 0 0
\(577\) 39.6102 1.64900 0.824498 0.565866i \(-0.191458\pi\)
0.824498 + 0.565866i \(0.191458\pi\)
\(578\) 0 0
\(579\) −30.6270 −1.27282
\(580\) 0 0
\(581\) −3.48532 −0.144596
\(582\) 0 0
\(583\) −6.35917 −0.263370
\(584\) 0 0
\(585\) −0.138336 −0.00571950
\(586\) 0 0
\(587\) −45.5309 −1.87926 −0.939631 0.342188i \(-0.888832\pi\)
−0.939631 + 0.342188i \(0.888832\pi\)
\(588\) 0 0
\(589\) −37.8596 −1.55998
\(590\) 0 0
\(591\) −31.2757 −1.28651
\(592\) 0 0
\(593\) −14.1339 −0.580408 −0.290204 0.956965i \(-0.593723\pi\)
−0.290204 + 0.956965i \(0.593723\pi\)
\(594\) 0 0
\(595\) −0.256512 −0.0105159
\(596\) 0 0
\(597\) −14.8867 −0.609272
\(598\) 0 0
\(599\) 18.9941 0.776077 0.388039 0.921643i \(-0.373153\pi\)
0.388039 + 0.921643i \(0.373153\pi\)
\(600\) 0 0
\(601\) −24.8536 −1.01380 −0.506899 0.862005i \(-0.669208\pi\)
−0.506899 + 0.862005i \(0.669208\pi\)
\(602\) 0 0
\(603\) −3.02807 −0.123313
\(604\) 0 0
\(605\) −0.216819 −0.00881495
\(606\) 0 0
\(607\) −32.1691 −1.30570 −0.652852 0.757486i \(-0.726427\pi\)
−0.652852 + 0.757486i \(0.726427\pi\)
\(608\) 0 0
\(609\) 7.99850 0.324116
\(610\) 0 0
\(611\) −3.51062 −0.142025
\(612\) 0 0
\(613\) 38.8049 1.56732 0.783658 0.621192i \(-0.213351\pi\)
0.783658 + 0.621192i \(0.213351\pi\)
\(614\) 0 0
\(615\) −2.65211 −0.106943
\(616\) 0 0
\(617\) 10.1541 0.408788 0.204394 0.978889i \(-0.434478\pi\)
0.204394 + 0.978889i \(0.434478\pi\)
\(618\) 0 0
\(619\) 1.67915 0.0674908 0.0337454 0.999430i \(-0.489256\pi\)
0.0337454 + 0.999430i \(0.489256\pi\)
\(620\) 0 0
\(621\) −6.82957 −0.274061
\(622\) 0 0
\(623\) 3.11011 0.124604
\(624\) 0 0
\(625\) 24.2971 0.971882
\(626\) 0 0
\(627\) 12.1161 0.483870
\(628\) 0 0
\(629\) 10.1960 0.406543
\(630\) 0 0
\(631\) −21.3599 −0.850323 −0.425161 0.905118i \(-0.639783\pi\)
−0.425161 + 0.905118i \(0.639783\pi\)
\(632\) 0 0
\(633\) 13.7941 0.548265
\(634\) 0 0
\(635\) −0.239584 −0.00950761
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 8.75716 0.346428
\(640\) 0 0
\(641\) 15.7163 0.620755 0.310378 0.950613i \(-0.399544\pi\)
0.310378 + 0.950613i \(0.399544\pi\)
\(642\) 0 0
\(643\) 10.1370 0.399766 0.199883 0.979820i \(-0.435944\pi\)
0.199883 + 0.979820i \(0.435944\pi\)
\(644\) 0 0
\(645\) −1.30372 −0.0513339
\(646\) 0 0
\(647\) −36.0162 −1.41594 −0.707972 0.706241i \(-0.750390\pi\)
−0.707972 + 0.706241i \(0.750390\pi\)
\(648\) 0 0
\(649\) 4.23350 0.166179
\(650\) 0 0
\(651\) 7.38054 0.289266
\(652\) 0 0
\(653\) −23.4509 −0.917705 −0.458853 0.888512i \(-0.651739\pi\)
−0.458853 + 0.888512i \(0.651739\pi\)
\(654\) 0 0
\(655\) 2.91659 0.113961
\(656\) 0 0
\(657\) −10.2833 −0.401192
\(658\) 0 0
\(659\) −43.1008 −1.67897 −0.839484 0.543384i \(-0.817143\pi\)
−0.839484 + 0.543384i \(0.817143\pi\)
\(660\) 0 0
\(661\) −40.7391 −1.58457 −0.792285 0.610152i \(-0.791108\pi\)
−0.792285 + 0.610152i \(0.791108\pi\)
\(662\) 0 0
\(663\) 1.81822 0.0706139
\(664\) 0 0
\(665\) −1.70932 −0.0662844
\(666\) 0 0
\(667\) 6.35713 0.246149
\(668\) 0 0
\(669\) −22.3482 −0.864030
\(670\) 0 0
\(671\) 0.624073 0.0240921
\(672\) 0 0
\(673\) −10.4837 −0.404118 −0.202059 0.979373i \(-0.564763\pi\)
−0.202059 + 0.979373i \(0.564763\pi\)
\(674\) 0 0
\(675\) −27.6930 −1.06591
\(676\) 0 0
\(677\) −50.8887 −1.95581 −0.977905 0.209049i \(-0.932963\pi\)
−0.977905 + 0.209049i \(0.932963\pi\)
\(678\) 0 0
\(679\) −3.26128 −0.125157
\(680\) 0 0
\(681\) 11.8302 0.453333
\(682\) 0 0
\(683\) 31.7447 1.21468 0.607338 0.794443i \(-0.292237\pi\)
0.607338 + 0.794443i \(0.292237\pi\)
\(684\) 0 0
\(685\) −1.11382 −0.0425570
\(686\) 0 0
\(687\) −33.8104 −1.28995
\(688\) 0 0
\(689\) −6.35917 −0.242265
\(690\) 0 0
\(691\) −23.9350 −0.910532 −0.455266 0.890356i \(-0.650456\pi\)
−0.455266 + 0.890356i \(0.650456\pi\)
\(692\) 0 0
\(693\) 0.638026 0.0242366
\(694\) 0 0
\(695\) −0.690589 −0.0261956
\(696\) 0 0
\(697\) −9.41598 −0.356656
\(698\) 0 0
\(699\) −29.4996 −1.11578
\(700\) 0 0
\(701\) 40.4956 1.52950 0.764748 0.644329i \(-0.222863\pi\)
0.764748 + 0.644329i \(0.222863\pi\)
\(702\) 0 0
\(703\) 67.9433 2.56253
\(704\) 0 0
\(705\) 1.16982 0.0440579
\(706\) 0 0
\(707\) 11.7866 0.443281
\(708\) 0 0
\(709\) 41.3601 1.55331 0.776655 0.629926i \(-0.216915\pi\)
0.776655 + 0.629926i \(0.216915\pi\)
\(710\) 0 0
\(711\) −8.34778 −0.313066
\(712\) 0 0
\(713\) 5.86599 0.219683
\(714\) 0 0
\(715\) −0.216819 −0.00810857
\(716\) 0 0
\(717\) −10.3656 −0.387112
\(718\) 0 0
\(719\) −35.2601 −1.31498 −0.657490 0.753464i \(-0.728382\pi\)
−0.657490 + 0.753464i \(0.728382\pi\)
\(720\) 0 0
\(721\) −15.9517 −0.594073
\(722\) 0 0
\(723\) 24.8836 0.925429
\(724\) 0 0
\(725\) 25.7774 0.957348
\(726\) 0 0
\(727\) −52.5398 −1.94859 −0.974297 0.225268i \(-0.927674\pi\)
−0.974297 + 0.225268i \(0.927674\pi\)
\(728\) 0 0
\(729\) 30.0400 1.11259
\(730\) 0 0
\(731\) −4.62870 −0.171199
\(732\) 0 0
\(733\) −51.6413 −1.90742 −0.953708 0.300734i \(-0.902768\pi\)
−0.953708 + 0.300734i \(0.902768\pi\)
\(734\) 0 0
\(735\) 0.333223 0.0122911
\(736\) 0 0
\(737\) −4.74600 −0.174821
\(738\) 0 0
\(739\) −31.1117 −1.14446 −0.572231 0.820093i \(-0.693922\pi\)
−0.572231 + 0.820093i \(0.693922\pi\)
\(740\) 0 0
\(741\) 12.1161 0.445096
\(742\) 0 0
\(743\) 10.4366 0.382883 0.191442 0.981504i \(-0.438684\pi\)
0.191442 + 0.981504i \(0.438684\pi\)
\(744\) 0 0
\(745\) 2.00753 0.0735503
\(746\) 0 0
\(747\) 2.22373 0.0813620
\(748\) 0 0
\(749\) −4.08272 −0.149179
\(750\) 0 0
\(751\) −33.0188 −1.20487 −0.602437 0.798166i \(-0.705804\pi\)
−0.602437 + 0.798166i \(0.705804\pi\)
\(752\) 0 0
\(753\) 13.3924 0.488045
\(754\) 0 0
\(755\) 1.40713 0.0512109
\(756\) 0 0
\(757\) 33.0313 1.20054 0.600272 0.799796i \(-0.295059\pi\)
0.600272 + 0.799796i \(0.295059\pi\)
\(758\) 0 0
\(759\) −1.87727 −0.0681407
\(760\) 0 0
\(761\) 47.9565 1.73842 0.869211 0.494441i \(-0.164627\pi\)
0.869211 + 0.494441i \(0.164627\pi\)
\(762\) 0 0
\(763\) −8.93859 −0.323599
\(764\) 0 0
\(765\) 0.163661 0.00591718
\(766\) 0 0
\(767\) 4.23350 0.152863
\(768\) 0 0
\(769\) −31.6963 −1.14300 −0.571498 0.820603i \(-0.693638\pi\)
−0.571498 + 0.820603i \(0.693638\pi\)
\(770\) 0 0
\(771\) 33.2250 1.19657
\(772\) 0 0
\(773\) −4.39679 −0.158141 −0.0790707 0.996869i \(-0.525195\pi\)
−0.0790707 + 0.996869i \(0.525195\pi\)
\(774\) 0 0
\(775\) 23.7858 0.854412
\(776\) 0 0
\(777\) −13.2452 −0.475170
\(778\) 0 0
\(779\) −62.7453 −2.24808
\(780\) 0 0
\(781\) 13.7254 0.491133
\(782\) 0 0
\(783\) −29.0988 −1.03991
\(784\) 0 0
\(785\) −2.25486 −0.0804794
\(786\) 0 0
\(787\) 32.2163 1.14839 0.574193 0.818720i \(-0.305316\pi\)
0.574193 + 0.818720i \(0.305316\pi\)
\(788\) 0 0
\(789\) 25.9168 0.922661
\(790\) 0 0
\(791\) 7.43235 0.264264
\(792\) 0 0
\(793\) 0.624073 0.0221615
\(794\) 0 0
\(795\) 2.11902 0.0751540
\(796\) 0 0
\(797\) 9.19579 0.325731 0.162866 0.986648i \(-0.447926\pi\)
0.162866 + 0.986648i \(0.447926\pi\)
\(798\) 0 0
\(799\) 4.15330 0.146933
\(800\) 0 0
\(801\) −1.98433 −0.0701129
\(802\) 0 0
\(803\) −16.1174 −0.568772
\(804\) 0 0
\(805\) 0.264842 0.00933447
\(806\) 0 0
\(807\) −12.2309 −0.430548
\(808\) 0 0
\(809\) 31.6701 1.11346 0.556731 0.830693i \(-0.312055\pi\)
0.556731 + 0.830693i \(0.312055\pi\)
\(810\) 0 0
\(811\) 22.2343 0.780752 0.390376 0.920655i \(-0.372345\pi\)
0.390376 + 0.920655i \(0.372345\pi\)
\(812\) 0 0
\(813\) −4.07189 −0.142808
\(814\) 0 0
\(815\) 3.38666 0.118629
\(816\) 0 0
\(817\) −30.8443 −1.07910
\(818\) 0 0
\(819\) 0.638026 0.0222944
\(820\) 0 0
\(821\) 22.0362 0.769068 0.384534 0.923111i \(-0.374362\pi\)
0.384534 + 0.923111i \(0.374362\pi\)
\(822\) 0 0
\(823\) 7.29612 0.254327 0.127163 0.991882i \(-0.459413\pi\)
0.127163 + 0.991882i \(0.459413\pi\)
\(824\) 0 0
\(825\) −7.61211 −0.265020
\(826\) 0 0
\(827\) 13.7818 0.479242 0.239621 0.970867i \(-0.422977\pi\)
0.239621 + 0.970867i \(0.422977\pi\)
\(828\) 0 0
\(829\) −10.1029 −0.350888 −0.175444 0.984489i \(-0.556136\pi\)
−0.175444 + 0.984489i \(0.556136\pi\)
\(830\) 0 0
\(831\) 24.3279 0.843926
\(832\) 0 0
\(833\) 1.18307 0.0409909
\(834\) 0 0
\(835\) −3.76363 −0.130246
\(836\) 0 0
\(837\) −26.8506 −0.928093
\(838\) 0 0
\(839\) −9.01500 −0.311232 −0.155616 0.987818i \(-0.549736\pi\)
−0.155616 + 0.987818i \(0.549736\pi\)
\(840\) 0 0
\(841\) −1.91415 −0.0660051
\(842\) 0 0
\(843\) −21.0963 −0.726595
\(844\) 0 0
\(845\) −0.216819 −0.00745880
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 50.8904 1.74655
\(850\) 0 0
\(851\) −10.5272 −0.360867
\(852\) 0 0
\(853\) −49.8042 −1.70526 −0.852631 0.522514i \(-0.824994\pi\)
−0.852631 + 0.522514i \(0.824994\pi\)
\(854\) 0 0
\(855\) 1.09059 0.0372973
\(856\) 0 0
\(857\) −10.8500 −0.370630 −0.185315 0.982679i \(-0.559331\pi\)
−0.185315 + 0.982679i \(0.559331\pi\)
\(858\) 0 0
\(859\) 12.2324 0.417364 0.208682 0.977984i \(-0.433083\pi\)
0.208682 + 0.977984i \(0.433083\pi\)
\(860\) 0 0
\(861\) 12.2319 0.416862
\(862\) 0 0
\(863\) −8.41335 −0.286394 −0.143197 0.989694i \(-0.545738\pi\)
−0.143197 + 0.989694i \(0.545738\pi\)
\(864\) 0 0
\(865\) 4.98972 0.169656
\(866\) 0 0
\(867\) 23.9757 0.814259
\(868\) 0 0
\(869\) −13.0838 −0.443836
\(870\) 0 0
\(871\) −4.74600 −0.160812
\(872\) 0 0
\(873\) 2.08078 0.0704239
\(874\) 0 0
\(875\) 2.15800 0.0729536
\(876\) 0 0
\(877\) 0.242393 0.00818503 0.00409252 0.999992i \(-0.498697\pi\)
0.00409252 + 0.999992i \(0.498697\pi\)
\(878\) 0 0
\(879\) 47.4536 1.60057
\(880\) 0 0
\(881\) −17.3393 −0.584176 −0.292088 0.956392i \(-0.594350\pi\)
−0.292088 + 0.956392i \(0.594350\pi\)
\(882\) 0 0
\(883\) 45.8842 1.54413 0.772063 0.635547i \(-0.219225\pi\)
0.772063 + 0.635547i \(0.219225\pi\)
\(884\) 0 0
\(885\) −1.41070 −0.0474201
\(886\) 0 0
\(887\) −53.7338 −1.80420 −0.902102 0.431523i \(-0.857976\pi\)
−0.902102 + 0.431523i \(0.857976\pi\)
\(888\) 0 0
\(889\) 1.10500 0.0370604
\(890\) 0 0
\(891\) 6.67884 0.223750
\(892\) 0 0
\(893\) 27.6764 0.926154
\(894\) 0 0
\(895\) 3.30210 0.110377
\(896\) 0 0
\(897\) −1.87727 −0.0626804
\(898\) 0 0
\(899\) 24.9932 0.833570
\(900\) 0 0
\(901\) 7.52333 0.250638
\(902\) 0 0
\(903\) 6.01294 0.200098
\(904\) 0 0
\(905\) 1.66595 0.0553782
\(906\) 0 0
\(907\) −3.15037 −0.104606 −0.0523032 0.998631i \(-0.516656\pi\)
−0.0523032 + 0.998631i \(0.516656\pi\)
\(908\) 0 0
\(909\) −7.52016 −0.249428
\(910\) 0 0
\(911\) 40.0568 1.32714 0.663571 0.748114i \(-0.269040\pi\)
0.663571 + 0.748114i \(0.269040\pi\)
\(912\) 0 0
\(913\) 3.48532 0.115347
\(914\) 0 0
\(915\) −0.207955 −0.00687479
\(916\) 0 0
\(917\) −13.4517 −0.444215
\(918\) 0 0
\(919\) 10.5917 0.349387 0.174694 0.984623i \(-0.444107\pi\)
0.174694 + 0.984623i \(0.444107\pi\)
\(920\) 0 0
\(921\) 47.5007 1.56520
\(922\) 0 0
\(923\) 13.7254 0.451777
\(924\) 0 0
\(925\) −42.6864 −1.40352
\(926\) 0 0
\(927\) 10.1776 0.334277
\(928\) 0 0
\(929\) 3.65036 0.119764 0.0598822 0.998205i \(-0.480927\pi\)
0.0598822 + 0.998205i \(0.480927\pi\)
\(930\) 0 0
\(931\) 7.88361 0.258375
\(932\) 0 0
\(933\) −33.1082 −1.08392
\(934\) 0 0
\(935\) 0.256512 0.00838882
\(936\) 0 0
\(937\) 34.2893 1.12018 0.560091 0.828431i \(-0.310766\pi\)
0.560091 + 0.828431i \(0.310766\pi\)
\(938\) 0 0
\(939\) 40.1581 1.31051
\(940\) 0 0
\(941\) 32.1415 1.04778 0.523891 0.851785i \(-0.324480\pi\)
0.523891 + 0.851785i \(0.324480\pi\)
\(942\) 0 0
\(943\) 9.72179 0.316585
\(944\) 0 0
\(945\) −1.21227 −0.0394353
\(946\) 0 0
\(947\) −23.8830 −0.776093 −0.388047 0.921640i \(-0.626850\pi\)
−0.388047 + 0.921640i \(0.626850\pi\)
\(948\) 0 0
\(949\) −16.1174 −0.523194
\(950\) 0 0
\(951\) 27.2860 0.884810
\(952\) 0 0
\(953\) −2.13519 −0.0691655 −0.0345828 0.999402i \(-0.511010\pi\)
−0.0345828 + 0.999402i \(0.511010\pi\)
\(954\) 0 0
\(955\) 4.88105 0.157947
\(956\) 0 0
\(957\) −7.99850 −0.258555
\(958\) 0 0
\(959\) 5.13711 0.165886
\(960\) 0 0
\(961\) −7.93775 −0.256057
\(962\) 0 0
\(963\) 2.60488 0.0839411
\(964\) 0 0
\(965\) −4.32080 −0.139092
\(966\) 0 0
\(967\) −47.5940 −1.53052 −0.765261 0.643720i \(-0.777390\pi\)
−0.765261 + 0.643720i \(0.777390\pi\)
\(968\) 0 0
\(969\) −14.3342 −0.460479
\(970\) 0 0
\(971\) −6.66802 −0.213987 −0.106993 0.994260i \(-0.534122\pi\)
−0.106993 + 0.994260i \(0.534122\pi\)
\(972\) 0 0
\(973\) 3.18510 0.102110
\(974\) 0 0
\(975\) −7.61211 −0.243783
\(976\) 0 0
\(977\) −8.35855 −0.267414 −0.133707 0.991021i \(-0.542688\pi\)
−0.133707 + 0.991021i \(0.542688\pi\)
\(978\) 0 0
\(979\) −3.11011 −0.0993996
\(980\) 0 0
\(981\) 5.70306 0.182085
\(982\) 0 0
\(983\) 15.9127 0.507536 0.253768 0.967265i \(-0.418330\pi\)
0.253768 + 0.967265i \(0.418330\pi\)
\(984\) 0 0
\(985\) −4.41232 −0.140588
\(986\) 0 0
\(987\) −5.39537 −0.171737
\(988\) 0 0
\(989\) 4.77903 0.151964
\(990\) 0 0
\(991\) 38.5861 1.22573 0.612863 0.790189i \(-0.290018\pi\)
0.612863 + 0.790189i \(0.290018\pi\)
\(992\) 0 0
\(993\) −9.75331 −0.309512
\(994\) 0 0
\(995\) −2.10019 −0.0665805
\(996\) 0 0
\(997\) 52.4700 1.66174 0.830871 0.556465i \(-0.187843\pi\)
0.830871 + 0.556465i \(0.187843\pi\)
\(998\) 0 0
\(999\) 48.1865 1.52455
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))